A371005 - OEIS

%I #11 Nov 07 2024 10:54:29

%S 1,2,10,86,1074,17742,366026,9074102,263006050,8732015390,

%T 326876957562,13624410416454,625859432308754,31418430350730542,

%U 1711378030988087338,100535991279811936982,6336275006902469756610,426480351471985076800062

%N Expansion of e.g.f. (1/x) * Series_Reversion( x/(2*exp(x) - 1) ).

%H <a href="/index/Res#revert">Index entries for reversions of series</a>

%F a(n) = 1/(n+1) * Sum_{k=0..n+1} 2^k * (-1)^(n+1-k) * k^n * binomial(n+1,k).

%F a(n) = n! * Sum_{k=0..n} 2^k * Stirling2(n,k)/(n-k+1)!. - _Seiichi Manyama_, Nov 07 2024

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x/(2*exp(x)-1))/x))

%o (PARI) a(n) = sum(k=0, n+1, 2^k*(-1)^(n+1-k)*k^n*binomial(n+1, k))/(n+1);

%Y Cf. A000272, A371006.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 08 2024